This is a place to put examples of everyone's favorite complete inner product space. Real spaces are only listed if both real and complex are common.
- All real and complex finite dimensional vector spaces
- \(L^2(\Omega)\) like \(L^2(\mathcal{R})\) and \(L^2[0, 1]\)
- Weighted \(L^2\) by integrating with another \(L^2\) function.
- \(l^2\) isomorphic to all infinite-dimensional separable hilbert spaces
- \(H^s\)(\Omega)\( is $L^2\) functions with \(s\) weak-derivatives in \(L^2\)
- Hardy space are holomorphic functions on unit disk whose power series converges at \(r = 1\).
- Bergman space are holomorphic functions that are in \(L^2\).
- Harmonic functions on the unit ball.
- Reproducing kernel hilbert spaces generated by positive-definite kernels
- Reproducing kernel hilbert spaces generateed by feature maps
- Fock space